Students need opportunities to read about, represent, view, write about, listen to and discuss mathematical ideas. These opportunities allow students to create links between their own language and ideas, and the formal language and symbols of mathematics. Communication is important in clarifying, reinforcing and modifying ideas, attitudes and beliefs about mathematics. Students should be encouraged to use a variety of forms of communication while learning mathematics. Students also need to communicate their learning using mathematical terminology. Communication helps students make connections among concrete, pictorial, symbolic, oral, written and mental representations of mathematical ideas.
Student talk is important across all grade levels. Students need to talk about and talk through mathematical concepts, with one another and with the teacher.
Representations of concepts promote understanding and communication. Representations of concepts can take a variety of forms (e.g., manipulatives, pictures, diagrams, or symbols). Children who use manipulatives or pictorial materials to represent a mathematical concept are more likely to understand the concept. Children’s attitudes towards mathematics are improved when teachers effectively use manipulatives to teach difficult concepts (Sowell, 1989; Thomson & Lambdin, 1994). However, students need to be guided in their experiences with concrete and visual representations, so that they make the appropriate links between the mathematical concept and the symbols and language with which it is represented.
Problem solving should be the basis for most mathematical learning. Problem-solving situations provide students with interesting contexts for learning mathematics and give students an understanding of the relevancy of mathematics. Even very young children benefit from learning in problem solving contexts. Learning basic facts through a problem-solving format, in relevant and meaningful contexts, is much more significant to children than memorizing facts without purpose.
Students need frequent experiences using a variety of resources and learning strategies (e.g., number lines, hundreds charts or carpets, base ten blocks, interlocking cubes, ten frames, calculators, math games, math songs, physical movement, math stories). Some strategies (e.g., using math songs, using movement) may not overtly involve children in problem solving; nevertheless, they should be used in instruction because they address the learning styles of many children, especially in the primary grades.
As students confront increasingly more complex concepts, they need to be encouraged to use their reasoning skills. It is important for students to realize that math “makes sense” and that they have the skills to navigate. Students should be encouraged to use reasoning skills such as looking for patterns and making estimates.
Explanation of justification of mathematical concepts, procedures, and problem solving
Provides incomplete or inaccurate explanations/justifications that lack clarity or logical thought, using minimal words, pictures, symbols, and/or numbers
Provides partial explanations/justifications that exhibit some clarity and logical thought, using simple words, pictures,symbols, and/or numbers.
Provides complete, clear, and logical explanations/ justifications, using appropriate words, pictures, symbols, and/or numbers.
Provides thorough, clear, and insightful explanations/ Justifications, using a arrange of words, pictures, symbols, and/or numbers.
Organization of Material (written, spoken or drawn)
Organization is minimal and seriously impedes communication.
Organization is limited but does not seriously impede communication.
Organization is sufficient to support communication.
Organization is effective and aids communication.
Use of Mathematical Vocabulary
Uses very little mathematical vocabulary, and vocabulary used lacks clarity and precision.
Uses a limited range of mathematical vocabulary with some degree of clarity and precision.
Uses mathematical vocabulary with sufficient clarity and precision to communicate ideas.
Uses a broad range of mathematical vocabulary to communicate clearly and precisely.
Use of Mathematical Representations (graphs, charts, or diagrams)
Uses representations that exhibit minimal clarity and accuracy, and are ineffective in communicating.
Uses representations that lack clarity and accuracy, though not sufficient to impede communication.
Uses representations that are sufficiently clear and accurate to communicate.
Uses representations that are clear, precise and effective in communicating.
Use of Mathematical Conventions (units, symbols, or labels)
Brief Explanation
(Alberta Program of Studies)Students need opportunities to read about, represent, view, write about, listen to and discuss mathematical ideas. These opportunities allow students to create links between their own language and ideas, and the formal language and symbols of mathematics.
Communication is important in clarifying, reinforcing and modifying ideas, attitudes and beliefs about mathematics. Students should be encouraged to use a variety of forms of communication while learning mathematics. Students also need to communicate their learning using mathematical terminology.
Communication helps students make connections among concrete, pictorial, symbolic, oral, written and mental representations of mathematical ideas.
Research
Characteristics of a Numerate Individual
- Student talk is important across all grade levels. Students need to talk about and talk through mathematical concepts, with one another and with the teacher.
- Representations of concepts promote understanding and communication. Representations of concepts can take a variety of forms (e.g., manipulatives, pictures, diagrams, or symbols). Children who use manipulatives or pictorial materials to represent a mathematical concept are more likely to understand the concept. Children’s attitudes towards mathematics are improved when teachers effectively use manipulatives to teach difficult concepts (Sowell, 1989; Thomson & Lambdin, 1994). However, students need to be guided in their experiences with concrete and visual representations, so that they make the appropriate links between the mathematical concept and the symbols and language with which it is represented.
- Problem solving should be the basis for most mathematical learning. Problem-solving situations provide students with interesting contexts for learning mathematics and give students an understanding of the relevancy of mathematics. Even very young children benefit from learning in problem solving contexts. Learning basic facts through a problem-solving format, in relevant and meaningful contexts, is much more significant to children than memorizing facts without purpose.
- Students need frequent experiences using a variety of resources and learning strategies (e.g., number lines, hundreds charts or carpets, base ten blocks, interlocking cubes, ten frames, calculators, math games, math songs, physical movement, math stories). Some strategies (e.g., using math songs, using movement) may not overtly involve children in problem solving; nevertheless, they should be used in instruction because they address the learning styles of many children, especially in the primary grades.
- As students confront increasingly more complex concepts, they need to be encouraged to use their reasoning skills. It is important for students to realize that math “makes sense” and that they have the skills to navigate. Students should be encouraged to use reasoning skills such as looking for patterns and making estimates.
http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_3_NSN.pdfClearly Identified Key Outcomes
http://www.learnalberta.ca/ProgramOfStudy.aspx?ProgramId=26061#1) Number Sense
2) Patterns and Relations
3) Shape and Space
4) Statistics and Probability
Balanced Assessment Practices
Sample Communication Rubric
Justifications, using a arrange of words, pictures, symbols, and/or numbers.
Purposeful Instructional Strategies
Personalization of Learning